The ratio test and root test are two of the most common tests to use to determine if a series is convergent or divergent. The ratio test involves taking the limit of a ratio and the root test involves taking the limit of a root. The ratio test is advisable when the n-th term of the series involves n!, a^n, nor n^n where a is a constant. The root test is advisable when the n-th term of the series involves a power containing n.

Objectives

By the end of this topic you should know and be prepared to be tested on:

11.6.1 Understand the conditions necessary to apply the ratio test and know the types of series for which the ratio test is a good choice

11.6.2 Know how to use the ratio test accurately to determine the convergence or divergence of a series

11.6.3 Understand when the ratio test is inconclusive

11.6.4 Understand the conditions necessary to apply the root test and know the types of series for which the root test is a good choice

11.6.5 Know how to use the root test accurately to determine the convergence or divergence of a series